How many ways can Hannah give 3 of her 8 T-shirts to her younger sister?
Do you multiply 8*3?
use the 8C3.now, can u evaluate the value of 8C3 ?.nCr = n!/r!(n-r)!it is the general formula of combination. also u have know about the "factorial", like
3! = 3 * 2 * 1 = 6
8C3, in this case knowed n=8 and r=3. by using the formula above, it can be
8C3 = 8!/3!(8-3)! = 8!/3!5! = 8 * 7 * 6 * 5! / 3*2*1*5! (cancel out the 5!)
= 8 * 7 * 6 / 3 * 2 * 1 = 8*7*6/6 (cancel out the 6) = 8 * 7 = 56
there are 56 ways
No, to find the number of ways Hannah can give 3 of her 8 T-shirts to her younger sister, we need to use the concept of combinations.
The formula for finding the number of combinations is given by:
C(n, r) = n! / (r!(n-r)!),
where n represents the total number of T-shirts (8 in this case) and r represents the number of T-shirts to be given to her sister (3 in this case). The exclamation mark (!) denotes the factorial of a number.
Therefore, to calculate the number of ways Hannah can give 3 T-shirts to her sister, we substitute the values into the formula:
C(8, 3) = 8! / (3!(8-3)!)
Simplifying further:
C(8, 3) = 8! / (3! * 5!)
Next, calculate the factorials:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
3! = 3 * 2 * 1 = 6
5! = 5 * 4 * 3 * 2 * 1 = 120
Now, substitute the values back into the equation:
C(8, 3) = 40,320 / (6 * 120)
C(8, 3) = 40,320 / 720
C(8, 3) = 56
Therefore, there are 56 different ways Hannah can give 3 of her 8 T-shirts to her younger sister.